Special equipment: a 3 1/2-inch ramekin
Pulse together the cream cheese, sugar, vanilla extract and salt in a food processor until smooth. Add the flour and butter and pulse until the dough just comes together in a solid mass (chunks of butter should be visible), about 6 to 8 long pulses. Shape the dough into a rectangle about 1/2-inch-thick. Wrap in plastic wrap and refrigerate until firm, at least 1 hour. Wipe out the food processor.
Meanwhile, make the filling: Combine the figs, raspberry jam and juice in a small saucepan. Bring to a simmer over medium-low heat and cook, stirring frequently, until the figs are plump and the juice is syrupy, about 25 minutes. Remove from heat and cool slightly. Puree in the food processor until smooth and set aside to cool completely.
Preheat the oven to 375 degrees F. Generously spray the back side of a baking sheet with cooking spray and set aside.
Put the chilled dough between 2 pieces of parchment. Roll out the dough into an 11-by-13-inch rectangle and 1/8-inch-thick (see Cook's Note). Refrigerate until firm, about 30 minutes. Remove the top piece of the parchment, to free it from the dough, then place it back on top. Turn the dough over and remove the top piece of parchment. Spread the fig mixture evenly over the dough.
Roll the dough into a log using the parchment as a guide (the dough is very soft and the parchment will make it easier to roll). Transfer the log to the prepared baking sheet, brush with the egg wash and coat with the sanding sugar. Cut 20 slits across the log, about 1/2-inch apart. Each slit should go about three-quarters of the way through the log so that it is still completely intact. Bend about a quarter of the log by turning some of the newly cut "tabs" out so that the pinwheels of filling are facing up. Continue turning the "tabs" out and bending the log until you have a ring. Butt the ends up against each other.
Spray the outside of a 3 1/2-inch round ramekin with cooking spray and place in the center of the ring. Chill the shaped rugelach dough for 30 minutes. Bake until cooked through and golden brown, 30 to 35 minutes.
Remove the ramekin and let the ring cool for 5 minutes then slide a flat spatula underneath to free the ring from the baking sheet. Gently slide the ring onto a cooling rack and let cool completely before serving.
When measuring flour, we spoon it into a dry measuring cup and level off excess. (Scooping directly from the bag compacts the flour, resulting in dry baked goods.) To ensure even rolling you, you can purchase rolling pin bands, which help provide the perfect amount of space between your rolling pin and countertop. For this particular recipe, be sure to use 1/8-inch bands.
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